Balbharati Maharashtra State Board12th Commerce Maths Digest PdfChapter 3 Linear Regression Ex 3.1 Questions and Answers.
Maharashtra State Board 12th Commerce Maths Solutions Chapter 3 Linear Regression Ex 3.1
Question 1
Maharashtra Board Solution
The HRD manager of the company wants to find a measure which he can use to fix the monthly income of persons applying for the job in the production department. As an experimental project. He collected data of 7 persons from that department referring to years of service and their monthly incomes. (i) Find the regression equation of income on years of service. (ii) What initial start would you recommend for a person applying for the job after having served in a similar capacity in another company for 13 years?
Solution & Step-by-Step Answer:
(i) Regression equation of Y on X is (Y – ) = byx (x – ) (Y – 8) = 0.75(x – ) Y = 0.75x + 2 (ii) When x = 13 Y = 0.75(13) + 2 = 11.75 Recommended income for the person is ₹ 11750.
Question 2
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Calculate the regression equations of X on Y and Y on X from the following date:
Solution & Step-by-Step Answer:
Regression equation of X on Y is (X – ) = bxy (Y – ) (X – 14) = 1(Y – 8) X – 14 = Y – 8 X = Y + 6 Regression equation Y on X is (Y – ) = byx (X – ) (Y – 8) = 0.87(X – 14) Y – 8 = 0.87X – 12.18 Y = 0.87X – 4.18
Question 3
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For a certain bivariate data on 5 pairs of observations given Σx = 20, Σy = 20, Σx2 = 90, Σy2 = 90, Σxy = 76 Calculate (i) cov(x, y), (ii) byx and bxy, (iii) r
Solution & Step-by-Step Answer:
Sine byx and bxy are negative, r = -0.4
Question 4
Maharashtra Board Solution
From the following data estimate y when x = 125
Solution & Step-by-Step Answer:
Let u = x – 122, v = y – 14 Regression equation of Y on X is (Y – ) = byx (X – ) (Y – 13.5) = -0.21(x – 121.5) Y – 13.5 = -0.21x + 25.52 Y = -0.21x + 39.02 When x = 125 Y = -0.21(125) + 39.02 = -26.25 + 39.02 = 12.77
Question 5
Maharashtra Board Solution
The following table gives the aptitude test scores and productivity indices of 10 works selected at workers selected randomly. Obtain the two regression equation and estimate (i) The productivity index of a worker whose test score is 95. (ii) The test score when productivity index is 75.
Solution & Step-by-Step Answer:
Regression equation of Y on X, (Y – ) = byx (X – ) (Y – 65) = 1.16 (x – 65) Y – 65 = 1.16x – 75.4 Y = 1.16x – 10.4 (i) When x = 95 Y = 1.16(95) – 10.4 = 110.2 – 10.4 = 99.8 Regression equation of X on Y, (X – ) = bxy (Y – ) (X – 65) = 0.59(y – 65) (X – 65) = 0.59y – 38.35 X = 0.59y + 26.65 (ii) When y = 75 x = 0.59(75) + 26.65 = 44.25 + 26.65 = 70.9
Question 6
Maharashtra Board Solution
Compute the appropriate regression equation for the following data.
Solution & Step-by-Step Answer:
Since x is the independent variable, and y is the dependent variable, we need to find regression equation of y on x Regression equation of y on x is (y – ) = byx (x – ) (y – 10) = -13.4(x – 6) y – 10 = -1.34x + 8.04 y = -1.34x + 18.04
Question 7
Maharashtra Board Solution
The following are the marks obtained by the students in Economic (X) and Mathematics (Y) Find the regression equation of Y and X.
Solution & Step-by-Step Answer:
Let u = x – 61, v = y – 80 Regression equation of Y on X is (Y – ) = byx (X – ) (Y – 80.4) = 0.3(x – 61) Y – 80.4 = 0.3x – 18.3 Y = 0.3x + 62.1
Question 8
Maharashtra Board Solution
For the following bivariate data obtain the equation of two regressions lines:
Solution & Step-by-Step Answer:
Regression equation of Y on X (Y – ) = byx (X – ) (Y – 9) = 2(x – 3) Y – 9 = 2x – 6 Y = 2x + 3 Regression equation of X on Y (X – ) = bxy (Y – ) (X – 3) = 0.5(y – 9) (X – 3) = 0.5y – 4.5 X = 0.5y – 1.5
Question 9
Maharashtra Board Solution
Find the following data obtain the equation of two regression lines:
Solution & Step-by-Step Answer:
Regression of Y on X, (Y – ) = byx (X – ) (Y – 8) = 0.65(x – 6) Y – 8 = -0.65x + 3.9 Y = -0.65x + 11.9 Regression of X on Y (X – ) = bxy (Y – ) (X – 6) = -1.3(y – 8) (X – 6) = -1.3y + 10.4 X = -1.3y + 16.4
Question 10
Maharashtra Board Solution
For the following data, find the regression line of Y on X Hence find the most likely value of y when x = 4
Solution & Step-by-Step Answer:
(Y – 3) = 2(x – 2) Y – 3 = 2x – 4 Y = 2x – 1 When x = 4 Y = 2(4) – 1 = 8 – 1 = 7
Question 11
Maharashtra Board Solution
Find the following data, find the regression equation of Y on X, and estimate Y when X = 10.
Solution & Step-by-Step Answer:
Regression equation of Y on X is (Y – ) = byx (X – ) (Y – 5) = (0.63)(x – 3.5) Y – 5 = 0.63x – 2.2 Y = 0.63x + 2.8 When x = 10 Y = 0.63(10) + 2.8 = 6.3 + 2.8 = 9.1
Question 12
Maharashtra Board Solution
The following sample gave the number of hours of study (X) per day for an examination and marks (Y) obtained by 12 students. Obtain the line of regression of marks on hours of study.
Solution & Step-by-Step Answer:
Let u = x – 5, v = y – 70 ∴ Equation of marks on hours of study is (Y – ) = byx (X – ) (Y – 70.83) = 6.6(x – 4.92) Y – 70.83 = 6.6x – 32.47 ∴ Y = 6.6x + 38.36
